There is an apparatus which acquires a cross-sectional image or a three-dimensional image of the inside of an object by receiving ultrasound waves from within the object. As an example of such an apparatus, there is a type which uses ultrasound waves for both transmission and reception; for instance, a type which transmits ultrasound waves and receives the reflected waves thereof. As a different example, there is a type which utilizes the photoacoustic effect in which the object that absorbed light energy is subject to adiabatic expansion and generates elastic waves (ultrasound waves) and transmits light energy into the object and receives the generated ultrasound waves; for instance, a type which uses light for transmission and uses ultrasound waves for reception.
Meanwhile, there is adaptive signal processing that has been developed in the field of radars. Adaptive signal processing is a processing method of adaptively changing the amplitude or phase of the respective signals according to the signals that were received at a plurality of receiving positions. For example, there is Constrained Minimization of Power (CMP) as one type of adaptive signal processing. This is a method where, upon receiving signals with a plurality of elements, processing is performed so as to minimize the signal power in a state of fixing the sensitivity related to a certain direction. With adaptive signal processing, the processing parameter of the received signal is adaptively changed for each such received signal. This kind of adaptive signal processing has the effect of improving the spatial resolution, in particular the resolution of the orientation direction.
Non Patent Literature 1 describes the results of improving the resolution by combining the foregoing adaptive signal processing with ultrasound waves, and Non Patent Literature 2 describes the results of imaging by combining the adaptive signal processing with photoacoustics.
As described in Non Patent Literatures 1 and 2, the spatial averaging method is used in order to inhibit the influence of interference waves having high correlation upon applying the CMP method to ultrasound received signals. Here, the spatial averaging method is a method of implementing adaptive processing by obtaining a correlation matrix from the received signals, and thereafter extracting a correlation submatrix obtained by extracting and averaging the submatrices.
Here, the processing upon applying adaptive signal processing to the received signals of the ultrasound waves is explained taking CMP as an example, and the necessity of using the spatial averaging method is thereafter explained.
Foremost, the process up to calculating the correlation matrix from the received signals is explained. Hilbert transformation is performed to the signals received by a plurality of elements and the received signals are subject to complex representation. Here, the s-th sample of the signals obtained by processing the received signals from the k-th element is set as xk[s], and the input vector X[s] of the s-th sample is defined as shown in Formula (1) below. Note that, here, M represents the total number of conversion elements. Moreover, T represents a transposed matrix.[Math. 1]X[s]=[x1[s],x2[s], . . . ,xM[s]]T  (1)
This input vector X[s] is used to calculate the correlation matrix Rxx as shown in Formula (2).
                    [                  Math          .                                          ⁢          2                ]                                                                                                                R                xx                            =                            ⁢                              E                ⁡                                  [                                                            X                      ⁡                                              [                        s                        ]                                                              ⁢                                                                  X                        H                                            ⁡                                              [                        s                        ]                                                                              ]                                                                                                        =                            ⁢                              (                                                                                                    E                        ⁡                                                  [                                                                                                                    x                                1                                                            ⁡                                                              [                                s                                ]                                                                                      ⁢                                                                                          x                                1                                *                                                            ⁡                                                              [                                s                                ]                                                                                                              ]                                                                                                                                    E                        ⁡                                                  [                                                                                                                    x                                1                                                            ⁡                                                              [                                s                                ]                                                                                      ⁢                                                                                          x                                2                                *                                                            ⁡                                                              [                                s                                ]                                                                                                              ]                                                                                                            …                                                                                      E                        ⁡                                                  [                                                                                                                    x                                1                                                            ⁡                                                              [                                s                                ]                                                                                      ⁢                                                                                          x                                M                                *                                                            ⁡                                                              [                                s                                ]                                                                                                              ]                                                                                                                                                                        E                        ⁡                                                  [                                                                                                                    x                                2                                                            ⁡                                                              [                                s                                ]                                                                                      ⁢                                                                                          x                                1                                *                                                            ⁡                                                              [                                s                                ]                                                                                                              ]                                                                                                                                    E                        ⁡                                                  [                                                                                                                    x                                2                                                            ⁡                                                              [                                s                                ]                                                                                      ⁢                                                                                          x                                2                                *                                                            ⁡                                                              [                                s                                ]                                                                                                              ]                                                                                                            …                                                                                      E                        ⁡                                                  [                                                                                                                    x                                2                                                            ⁡                                                              [                                s                                ]                                                                                      ⁢                                                                                          x                                M                                *                                                            ⁡                                                              [                                s                                ]                                                                                                              ]                                                                                                                                                ⋮                                                              ⋮                                                              ⋱                                                              ⋮                                                                                                                          E                        ⁡                                                  [                                                                                                                    x                                M                                                            ⁡                                                              [                                s                                ]                                                                                      ⁢                                                                                          x                                1                                *                                                            ⁡                                                              [                                s                                ]                                                                                                              ]                                                                                                                                    E                        ⁡                                                  [                                                                                                                    x                                M                                                            ⁡                                                              [                                s                                ]                                                                                      ⁢                                                                                          x                                2                                *                                                            ⁡                                                              [                                s                                ]                                                                                                              ]                                                                                                            …                                                                                      E                        ⁡                                                  [                                                                                                                    x                                M                                                            ⁡                                                              [                                s                                ]                                                                                      ⁢                                                                                          x                                M                                *                                                            ⁡                                                              [                                s                                ]                                                                                                              ]                                                                                                                    )                                                                        (        2        )            
The superscript H in the formula represents the complex conjugate transpose, and the superscript * represents the complex conjugate. E[ ] is the processing of calculating the time average, and represents that the average is calculated by changing the number (s in this example) of samples. The correlation matrix is obtained as described above.
Subsequently, the weight vector W based on the conditions of Formula (3) below is obtained.
                    [                  Math          .                                          ⁢          3                ]                                                                                                                                  min                  W                                ⁢                                                                  ⁢                                  (                                                            W                      H                                        ⁢                                          R                      xx                                        ⁢                    W                                    )                                                                                                                          subject                  ⁢                                                                          ⁢                  to                  ⁢                                                                          ⁢                                      W                    H                                    ⁢                  a                                =                1                                                    }                            (        3        )            
These conditions represent that the output power (WHRxxW) is minimized in a state where the sensitivity (WHa) in the intended direction is constrained to 1. Note that “a” is the steering vector, and defines the intended direction; that is, the observation direction.
The optimal weight Wopt is calculated from the foregoing conditions as shown in Formula (4).
                    [                  Math          .                                          ⁢          4                ]                                                            Wopt        =                                            R              xx                              -                1                                      ⁢            a                                              a              H                        ⁢                          R              xx                              -                1                                      ⁢            a                                              (        4        )            
As a result of using this optimal weight, the output power can be minimized in a state where the sensitivity of the intended direction is set to 1. The receiving arrays using this optimal weight form a receiving pattern in which the sensitivity of the intended direction, or the observation direction, is 1, and which has a directionality of low sensitivity relative to the arrival direction of the noise components.
Moreover, the power Pout from the intended direction can be represented as shown in Formula (5).
                    [                  Math          .                                          ⁢          5                ]                                                            Pout        =                  1                      2            ⁢                          a              H                        ⁢                          R              xx                              -                1                                      ⁢            a                                              (        5        )            
The basic principle of the CMP method is as described above.
In a general ultrasound imaging apparatus, a plurality of transmissions and receptions (typically 100 times or more) are performed upon generating one frame worth of a cross-sectional image while changing the transmitting/receiving direction or position. When acquiring a cross-sectional image or a three-dimensional image based on the transmission and reception of ultrasound waves as described above, the observation direction of the adaptive signal processing described above is generally caused to coincide with the transmitting direction of the ultrasound waves.
Meanwhile, although the foregoing principle is satisfied when the noise components and the intended waves have no correlativity, it is not satisfied when the noise components and the intended waves have correlativity. Specifically, when noise components having correlativity with the intended waves are received, formed is a receiving pattern of directionality having a sensitivity of 1 in the direction of the intended waves, but also an opposite phase sensitivity in the direction of the noise components. This is because, as a result of adding the noise components to the intended waves in an opposite phase in order to minimize the signals that are output, the output signals are caused to approach 0.
Meanwhile, when performing imaging by using the transmission/reception of ultrasound waves and the photoacoustic effect, the noise component is likely to have high correlativity with the intended component. For example, with imaging based on ultrasound waves, the reflected waves of the ultrasound waves that were transmitted on one's own are used in the imaging. Thus, the receives waves (i.e., noise components) that are reflected from directions other than the intended direction have high correlativity with the intended waves. Moreover, with imaging utilizing the photoacoustic effect also, the incident light spreads over a wide range due to the scattering effect, and the ultrasound waves generated from that wide range are likely to have high correlativity.
The spatial averaging method is the method of applying the CMP method even in cases where the correlativity of the intended components and noise components is high as described above. With the spatial averaging method, a plurality of submatrices are extracted from the foregoing correlation matrix, and the optimal weight is obtained by using the spatial average correlation matrix that is calculated based on the average of such submatrices.
The spatial average correlation matrix R′xx can be calculated with Formula (7) based on Formula (6) below relating to the correlation submatrix.
                    [                  Math          .                                          ⁢          6                ]                                                                                  X            n                    ⁡                      (            t            )                          =                              [                                                            x                  n                                ⁡                                  (                  t                  )                                            ,                                                x                                      n                    +                    1                                                  ⁡                                  (                  t                  )                                            ,              …              ⁢                                                          ,                                                x                                      n                    +                    K                    -                    1                                                  ⁡                                  (                  t                  )                                                      ]                    T                                    (        6        )                                          R          xx          ′                =                              ∑                          n              =              1                        N                    ⁢                                          ⁢                                    z              n                        ⁢                          E              ⁡                              [                                                                            X                      n                                        ⁡                                          (                      t                      )                                                        ⁢                                                            X                      n                      H                                        ⁡                                          (                      t                      )                                                                      ]                                                                        (        7        )            
Note that N is the number of submatrices to be extracted, and K is the size of the submatrices obtained based on M−N+1. Moreover, Zn is the weight coefficient upon averaging the submatrices, and, while this will be the simple average in the case of Zn=1/N, it is also possible to use the hamming window, the banning window, or the Dolph-Chebycheff window as the weighting function. Rnxx represents the submatrices in the correlation matrix Rxx moving on the diagonal components of Rxx and is a matrix having a size of K by K at a position where the (n, n) component of Rxx is the first diagonal component thereof. Zn is the coefficient upon adding the respective submatrices, and this is adjusted so that the sum of Zn becomes 1.
FIG. 1 is a diagram schematically representing the processing upon calculating the spatial average correlation matrix. The correlation matrix 001 of 9 by 9 is calculated based on the multiplication of the input signal vectors X (x1 to x9) and its complex conjugate vectors XH (x*1 to x*9). A plurality of correlation matrices associated with the lapse of the receiving time are averaged, and the processing for calculating the expectation of the correlation is performed. Subsequently, by extracting five submatrices 002 of 5 by 5 enclosed by the dotted line and obtaining the average thereof, a spatial average correlation matrix of 5 by 5 can be obtained.
As a result of using the spatial average correlation matrix calculated as described above, the foregoing optimal weight Wopt and the power Pout from the intended direction can be respectively calculated from Formula (8) and Formula (9) below.
                    [                  Math          .                                          ⁢          7                ]                                                            Wopt        =                                            R              xx                              ′                -                1                                      ⁢            a                                              a              H                        ⁢                          R              xx                              ′                -                1                                      ⁢            a                                              (        8        )                                Pout        =                  1                      2            ⁢                          a              H                        ⁢                          R              xx                              ′                -                1                                      ⁢            a                                              (        9        )            
The steering vector a in the foregoing case is a vector configured from K number of elements.
In the spatial averaging method, known is a correlation suppression factor which shows the effect of suppressing the correlativity interference waves as shown in Formula (10).
                    [                  Math          .                                          ⁢          8                ]                                                            ξ        =                              ∑                          n              =              1                        N                    ⁢                                          ⁢                      Zn            ⁢                                                  ⁢                          exp              [                              j                ⁢                                                      2                    ⁢                    π                    ⁢                                                                                  ⁢                    d                                    λ                                ⁢                                  (                                      n                    -                                                                  N                        +                        1                                            2                                                        )                                ⁢                                  (                                                            sin                      ⁢                                                                                          ⁢                      θ                      ⁢                                                                                          ⁢                      c                                        -                                          sin                      ⁢                                                                                          ⁢                      θ                      ⁢                                                                                          ⁢                      s                                                        )                                            ]                                                          (        10        )            ξ is the correlation suppression factor to be obtained,d is the distance between the adjacent elements,λ is the wavelength of the received signals,θs is the observing direction,θc is the arrival direction of the correlativity interference waves.
This formula is the same as the directionality synthesis of the N element linear array.
When this correlation suppression factor is small, the influence of the correlativity interference wave can be considerably suppressed.
Accordingly, with the CMP method, the correlation matrix and additionally the spatial average correlation matrix are obtained from the received signals, and the inverse matrix thereof can be used to calculate the complex weight or the power upon using the complex weight.
Since the distance from the position of the conversion elements can be set forth and the target direction can be defined by the steering vector depending on which sample of the received signals is used, the target position (distance and direction) in the object can be defined by the foregoing processing. The complex weight and the power upon using the complex weight are the weight and power upon setting the sensitivity relative to the signals from the target position to 1, and suppressing the signals arriving from other positions. In other words, signals from the target position can be selectively extracted with the CMP method and, consequently, the spatial resolution can be improved.
Note that, rather than directly obtaining the inverse matrix, calculation can also be performed based on the QR decomposition and the back substitution processing relative to the spatial average correlation matrix.
As a result of calculating the optimal weight by using the foregoing spatial average correlation matrix, even when noise components having high correlativity with the intended waves are received, the correlativity of that noise can be suppressed. Thus, even in cases where ultrasound waves are used for transmission and reception or when performing imaging using the photoacoustic effect, the effect of improving the spatial resolution of the orientation direction based on the CMP method is yielded.